Step-by-step statistical modeling analysis projects using data from physical science and engineering applications. Walks through data collection, data exploration, modeling and results interpretation.
Walks through analysis and modeling of a load cell output data with the goal of being able to understand performance characteristics of the cell and be able to predict future load output levels. exploratory data analysis, model fitting, heteroskedasticity tests and corrections, and interpretation of analysis results.
Load Cell Terminology
The zero conditional mean of errors Gauss-Markov assumption is like stating that there’s no relationship or linking mechanism between the stochastic error and any of the independent variables in that model
Having no serial correlation of errors is stating that the dependent variable in the sample observations from a population don’t affect or depend on each other.
Gauss-Markov – explanation of random sampling and serial correlation (Ben Lambert)
Understanding the Theory Behind Serial Correlation (Udemy Blog)
Covariance and Correlation (Random)
Serial correlation testing – introduction (Ben Lambert)
Weighted Least Squares adjusts the line of best fit plotting points taking into account a variable variance as the observation plot progresses. I.e. the regression in an area where there is lower variance will be “weighted” lower than an area where there’s a higher variance.
The weight is derived by taking the residual errors of the regression model and deriving a separate model of regression for that residual error, which describes a function of movement of how the error varies throughout the observations.
The derived weight is then applied as a multiplier to the regressor coefficients in the model.
Weighted Least Squares: an introduction (Ben Lambert)
Weighted Least Squares: mathematical introduction (Ben Lambert)
Weighted Least Squares: an example (Ben Lambert)
Weighted Least Squares in practice – feasible GLS – part 1 (Ben Lambert)
Weighted Least Squares in practice – feasible GLS – part 2 (Ben Lambert)
Weighted Least Squares Regression Process Modeling Method (NIST/SEMATECH e-Handbook of Statistical Methods)
Weighted Least Squares Regression Estimating Parameters (NIST/SEMATECH e-Handbook of Statistical Methods)
Weighted Least Squares (PennState STAT 501)
Weighted Least Squares Examples (PennState STAT 501)